Improvement of hydraulic flow analysis code for APWR ... › ... › papers › Aix_KasaharaCFD.pdffor APWR reactor internals F.Kasahara, S.Nakura, T.Morii, and Y. Nakadai Institute

Improvement of hydraulic flow analysis codefor APWR reactor internals

F.Kasahara, S.Nakura, T.Morii, and Y. Nakadai

Institute of Nuclear Safety (INS)Nuclear Power Engineering Corporation (NUPEC)

(PS) This study was performed under the sponsorship of METI

CFD Meeting Presentation Material in Aix en Provence, May 15-16, 2002

CFD meeting presentation 1

Contents

1.Background and Objectives2.Results of the hydraulic flow characteristics

analysis of reactor internals3.Results of the dynamic pressure analysis of

downcomer4.Conclusion


BackgroundSchedule of the project : Improvement of hydraulic flowanalysis code for APWR reactor internals

fiscal year 1996 1997 1998 1999 2000 2001 2002 2003i t em

ElectricTsuruga-3/4(APWR) Power Application� i� jNPPUtility plan forDevelopment

Coordination SafetyStart of operation : Council License

� ¤�¤2009 fiscal yearExpected)�i

Licensing schedule

Safety Review

Improve CFD(Computational Fluid Dynamics) codeSchedule of Project

Experiment

Design & roduce test facilityP

Investigation &Planning test facility


In safety review, it is necessary for the regulatory body todevelop its own analysis codes in order to independentlyevaluate the safety analysis results done by applicant.

One of the most innovative design improvement of APWR is the neutronreflector which replaces the conventional baffle-former structure.

Concerns:

• Coolability of the neutron reflector by heating

• Fluid-structure interaction (FSI) caused by dynamic pressure fluctuation

Develop analysis codes to evaluate the concerns.

Verification of analysis code based on the results of hydraulic flow test using1/5 scale mode.

Objectives


•••••Upper core plate

•••••••Lower core support plate

•••••Fuel assembly

•••••••

•••••••

••••

••••••

•••••

•••

•••••

••••

•••

•••••••

Flow pattern in APW R reactor vessel

Neutron reflector

Inlet nozzle

Core barrel

Reactor vessel

Outlet nozzle

main flow

by-pass flow

Lower core plate

Guide tube

Upper support column

Upper support plate


Developing analysis codes

Developing analysis codes utilizing IMPACT code modules item code remark

1 Coolability of the neutron reflector by

heating CFD-1

CFD-1 should be parallel simulation code with Reynolds averaged numerical simulation method (k- model).

2 Flow-induced vibration by dynamic pressure fluctuation

CFD-2 +

Structure- vibration analysis

code (FELIOS)

CFD-2 should be parallel simulation code with Large Eddy Simulation method or dynamic numerical simulation method.


Hydraulic flow analysis codes for APWR reactorinternals

• Hydraulic flow characteristics analysis of reactorinternals

Improvement of Reynolds averaged numerical simulation method (k-model) with unstructured grid• Dynamic pressure analysis of the downcomer Improvement of Large Eddy Simulation method with structured grid


Objective of hydraulic flow characteristicsanalysis of reactor internals

To establish the numerical method to exactlycalculate flow distribution into the neutron reflector

Measurement items in this experiment• Flow distribution into the neutron reflector• Pressure distribution on the lower core plate• Pressure distribution of the lower plenum


Calculation Conditions

Hydraulic flow characteristics analysis Analysis Case

Flow rate : 100 , Temperature : 150

Calculation Grid System Unstructured /or structured (BFC with Multi-block Methodl) Time Marching Method SIMPLE (Semi-Implicit Method-for Pressure-Linked Equation)

Turbulent Model k- model ( Reynolds averaged numerical simulation method)

Transient term Euler implicit Discretization

Convection term Donor-Cell method Density 917.0 [kg/m3]

Properties Viscosity 1.80 10-4 [Pa s] Inlet Constant : Vin=16.674 [m/s] Outlet Free out Boundary Condition Wall Log-Law


Velocity distribution in the Reactor vessel

90°180°90° - 270° cross section

velocitym/s

18

0

Velocity

m/s


0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 10 20 30 40

“± “ü E ”Ô †

”ñ \ ‘¢ Ši Žq

\ ‘¢ Ši Žq

ŽŽ Œ± Œ‹ ‰Ê�\‘¢Ši�q�i‚V‚V–œ�j

”ñ�\‘¢Ši�q�i‚U‚Q–œ�j

‰º•”˜F�S”ÂŒ`�ó�i��Œ±‘•’u�j

Flow distribution(Ratio to average)

••••••

Comparison between Calculation and Experiment

Structured grid

(770,000 meshes)

Unstructured grid

(620,000 meshes)

Unstructured

structured

experiment

Flow hole

Lower core plate

(test facility)Flow hole number

(Flow distribution into radial reflector)


0.7

0.8

0.9

1

1.1

1.2

1.3

0 5 10 15 20 25 30 35 40

• • • • •

•••••••••••••

•

• • • •• • • •

-6.0

-4.0

-2.0

0.0

2.0

4.0

6.0

8.0

0 5 10 15 20 25 30 35 40

• • • • • •••••••••••KPa•

• • • •

• • • •

Flow rate distribution into neutron reflector(ratio to average)

Pressure distribution on lower coreplate(deference from average kPa)


Flow hole No.Flow hole No.

AnalysisExperiment

Analysis

Experiment

(Flow and pressure distribution at the entrance of neutron reflector)


Experiment Calculation


0�‹

180�‹

270�‹ 90�‹

270�‹

0�‹

90�‹

180�‹

[k Pa]

(Pressure distribution in the lower plenum:bottom surface of test vessel)


Objective of dynamic pressure analysisof downcomer

Improve the code with LES to calculate adequately dynamicpressure by turbulent flow, selected in the 3-dimensional flowanalysis code which can simulate the model of flow passage.

To establish the numerical method tocalculate dynamic pressure induced byturbulent flow in downcomer.


Measuring Points of Dynamic Pressure

Upper

Middle

Lower

50mm

Circumferential point

Axial point

Reference point compared with experiment


Calculation Conditions

LES ( Analysis for optimized Cs value Analysis Case

Flow rate : 100 , Temperature : 150

Calculation Grid System BFC with Multi-block Method Time Marching Method SMAC ( Simplified Maker And Cell Method )

Turbulent Model LES (Smagorinsky eddy viscosity model : Cs=0.17 )

Transient term Euler Explicit Discretization Convection term QUICK Calculation of Time Interval 4.0 10-5 [s]

Density 917.0 [kg/m3] Properties

Viscosity 1.80 10-4 [Pa .s] Inlet Constant : Vin=16.674 [m/s] Outlet Sommerfeld Condition Boundary Condition Wall Log-Law


Calculation Grid

Calculation grid both side of wall

(a) Core Barrel (b) Reactor Vessel


Mean Velocity contour of downcomer

Calculation Results


[m/s][m/s]


Turbulent energy contour of downcomer


m2/s2 m2/s2

Calculation Results


Figure.4 Dynamic Pressure( 90 of downcomer see page 17 )

upper point middle point lower point

Calculate the dynamic pressure by turbulent flowto t = 0.6s. The data from t = 0.24s to t = 0.6s wasused in statistical analysis.

Calculation Results

- 50. 0

0. 0

50. 0

0. 0 0. 1 0. 2 0. 3 0. 4 0. 5 0. 6 0. 7

Š î� €̂ Ê’ u� ü• ûŒü‘ ŠŠ Ö̂ Ê’ u� ²• ûŒü‘ ŠŠ Ö̂ Ê’ u

ˆ³—

Í [k

Pa]

� �Š Ô [ s ]

- 50. 0

0. 0

50. 0

0. 0 0. 1 0. 2 0. 3 0. 4 0. 5 0. 6 0. 7


ˆ³—

Í [k

Pa]

� �Š Ô [ s ]

- 50. 0

0. 0

50. 0

0. 0 0. 1 0. 2 0. 3 0. 4 0. 5 0. 6 0. 7


ˆ³—

Í [k

Pa]

� �Š Ô [ s ]time [s] time [s] time [s]

time [s]

dyna

mic

pre

ssur

e [k

Pa]

dyna

mic

pre

ssur

e [k

Pa]

dyna

mic

pre

ssur

e [k

Pa]

dyna

mic

pre

ssur

e [k

Pa]reference pointcircumferential point

axial point

Experiment

reference pointcircumferential pointaxial point



RMS Value of Dynamic Pressure

( ) ( ) ( )fkfffPdffPpk

kkxx

f

f xxRMS∆⋅=∆⋅≅⋅= ∑∫

=

,~max

min

max

min

2( ) : C/E value

Calculation Results

1.6 1.45 0.9090 [deg]2.0 1.57 0.790 [deg]

Lower

1.8 2.50 1.3990 [deg]1.7 1.75 1.030 [deg]

Middle

5.0 6.49 1.30135 [deg]

5.011.75 2.3590 [deg]

4.9 6.20 1.2745 [deg]2.0 2.80 1.400 [deg]

Upper

ExperimentCalculationCircumferentialPositionAxial position


( ) ( )( ){ }∑ ∆⋅⋅

=

kxx

xxRMSxx

ffC

fCpfS2

~

Definition : RMS Spectrum

is the magnitude of Fourier coefficientxxC

RMSp~ is RMS value

Spectrum Analysis

Sampling cycle is 8 10-5 [s]

The spectrum is the ensembleaverage of Fourier coefficientcalculated by 2048 samples perone section.

( )fkf ∆⋅=

Calculation Results

CFD meeting presentation 25RMS Spectrum ( 90°of downcomer )

Upper point Middle point Lower point


0. 0

2. 5

5. 0

0 100 200 300 400 500

RMS

spec

trum

[k

Pa*s

0.5 ]

f r equency [ Hz]

0. 0

2. 5

5. 0

0 100 200 300 400 500

RMS

spec

trum

[k

Pa*s

0.5 ]

f r equency [ Hz]

0. 0

2. 5

5. 0

0 100 200 300 400 500

RMS

spec

trum

[k

Pa*s

0.5 ]

f r equency [ Hz]

Calculation Results

0. 0

2. 5

5. 0

0 100 200 300 400 500


‚q‚

l‚rƒ

Xƒyƒ

Nƒgƒ

‹ [k

Pa*s

0.5 ]

� ü” g� ” [ Hz]

0. 0

2. 5

5. 0

0 100 200 300 400 500


‚q‚

l‚rƒ

Xƒyƒ

Nƒgƒ

‹ [k

Pa*s

0.5 ]

� ü” g� ” [ Hz]

0. 0

2. 5

5. 0

0 100 200 300 400 500


‚q‚

l‚rƒ

Xƒyƒ

Nƒgƒ

‹ [k

Pa*s

0.5 ]

� ü” g� ” [ Hz]


RM

S sp

ectru

m [k

Pa×s

0.5 ]

Experiment

frequency [Hz] frequency [Hz] frequency [Hz]

RM

S sp

ectru

m [k

Pa×s

0.5 ]

RM

S sp

ectru

m [k

Pa×s

0.5 ]



Experiment Experiment


Definition : Normalized Cross-Spectrum

( ) ( )( ) ( )fPfP

fPf

yyxx

xyxy ⋅

=Γ( )fPxy( ) ( )fPfP yyxx ,

is real part of cross spectrumis power spectrum

Normalized Cross-Spectrum Approximated by Turbulent Theory**

‡ @ Axial Correlation

( )

−⋅⋅= −

C

fCxy U

yxfef πΓΓ 2cos10

*

‡ A Circumferential Correlation

( ) fCxy ef 10* −⋅= ΓΓ

**Taylor s hypothesis of frozen turbulence

Uc : Convection velocity is calculated form the peak of the cross-relation coefficient. C1 is approximated by the method of least squares using the normalized cross-spectrum raging the frequency shown by thick line.

Calculation Results


Normalized Cross Spectrum ( 90°of downcomer )

Calculation Results

- 1 . 0

- 0 . 5

0 . 0

0 . 5

1 . 0

0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0

–³�

ŸŒ³‰

»ƒNƒ

�ƒXƒ

Xƒyƒ

Nƒgƒ

‹

[�

|]

� ü” g� ” [ Hz ]

- 1 . 0

- 0 . 5

0 . 0

0 . 5

1 . 0

0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0

–³�

ŸŒ³‰

»ƒNƒ

�ƒXƒ

Xƒyƒ

Nƒgƒ

‹ [

�|]

� ü” g� ” [ Hz ]

- 1 . 0

- 0 . 5

0 . 0

0 . 5

1 . 0

0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0

–³�

ŸŒ³‰

»ƒNƒ

�ƒXƒ

Xƒyƒ

Nƒgƒ

‹ [�

|]

� ü” g� ” [ Hz ]

Cal

cula

tion

Cro

ss sp

ectr

um [-

]

Cro

ss sp

ectr

um [-

]

Cro

ss sp

ectr

um [-

]

Frequency [Hz] Frequency [Hz] Frequency [Hz]

Exp

erim

ent

Cro

ss sp

ectr

um [-

]

Cro

ss sp

ectr

um [-

]

Cro

ss sp

ectr

um [-

]

Frequency [Hz]Frequency [Hz]Frequency [Hz]




( ) ( )( ) ( )

00 ==⋅

=

ττττ

ττ

yyxx

xyxy

CC

CR ( )τxyC : cross-correlation function

: auto- correlation function( ) ( )ττ yyxx CC ,

Definition : Coefficient of Cross Correlation

Auto-Correlation Function Inverse-Fourier transform of power-spectrum

( ) ( ) dtefPC ftxxxx πτ 2−∞

∞−⋅= ∫

( ) ( ) dtefPC ftyyyy πτ 2−∞

∞−⋅= ∫

( ) ( ) dtefPC ftxyxy πτ 2−∞

∞−⋅= ∫

Cross-Correlation Function Inverse-Fourier transform of cross-spectrum

Calculation Results


Convection velocity

Calculation Results

9.410.7890 [deg]

6.28.800 [deg]Lower

9.98.9390 [deg]

5.9 9.190 [deg]Middle

9.58135 [deg]

12.612.0090 [deg]

9.8245 [deg]

5.4 7.380 [deg]

Upper

ExperimentCalculationCircumferentialPositionAxialposition


xy

yxΓ

−−=

lnλ

Definition : Correlation Length

xyΓ : Absolute normalized cross-spectrum approximated by turbulent theory

yx − : Distance between measuring point x to y (=50mm)

Calculation Results


Correlation length ( 90 deg Axial direction)

Calculation Results

0. 0

300. 0

600. 0

0 100 200 300 400 500

‘ŠŠ

Ö’·

[mm]

� ü” g� ” [ Hz]

0. 0

300. 0

600. 0

0 100 200 300 400 500

‘ŠŠ

Ö’·

[mm]

� ü” g� ” [ Hz]

0. 0

300. 0

600. 0

0 100 200 300 400 500

‘ŠŠ

Ö’·

[mm]

� ü” g� ” [ Hz]

Cal

cula

tion


Exp

erim

ent

Cor

rela

tion

leng

th [m

m]

Cor

rela

tion

leng

th [m

m]

Cor

rela

tion

leng

th [m

m]


Cor

rela

tion

leng

th [m

m]

Cor

rela

tion

leng

th [m

m]

Cor

rela

tion

leng

th [m

m]




0. 0

300. 0

600. 0

0 100 200 300 400 500

‘ŠŠ

Ö’·

[mm]

� ü” g� ” [ Hz]

0. 0

300. 0

600. 0

0 100 200 300 400 500

‘ŠŠ

Ö’·

[mm]

� ü” g� ” [ Hz]

0. 0

300. 0

600. 0

0 100 200 300 400 500

‘ŠŠ

Ö’·

[mm]

� ü” g� ” [ Hz]

Correlation length ( 90 deg Circumferential direction)

Calculation ResultsC

alcu

latio

n


Exp

erim

ent

Cor

rela

tion

leng

th [m

m]

Cor

rela

tion

leng

th [m

m]

Cor

rela

tion

leng

th [m

m]


Cor

rela

tion

leng

th [m

m]

Cor

rela

tion

leng

th [m

m]

Cor

rela

tion

leng

th [m

m]




Conclusion• CFD-1 with unstructured grids, SIMPLE method and k- turbulent model show good agreement with the experiments

data.• Considering present CFD technique, CFD-2 with structure

grids ( BFC method) , SMAC method and LES turbulentmodel is the best combination for the analysis of dynamicpressure fluctuation.

• Basically,CFD-1 and CFD-2 are applicable to plantoperating condition. For better evaluation, it is planed toconfirm that the numerical method of 1/5 scaled model isrightly applied to a real scale simulation.

Conclusion

Improvement of hydraulic flow analysis code for APWR reactor internalsHydraulic flow analysis codes for APWR reactor internalsObjective of hydraulic flow characteristics analysis of reactor internalsVelocity distribution in the Reactor vesselObjective of dynamic pressure analysis of downcomerConclusion

close:

Documents

Improvement of hydraulic flow analysis code for APWR ... › ... › papers › Aix_KasaharaCFD.pdffor APWR reactor internals F.Kasahara, S.Nakura, T.Morii, and Y. Nakadai Institute